Instrumental variables and interactions in the causal analysis of a complex clinical trial

We consider the application of instrumental variable techniques in a longitudinal clinical trial in paediatric HIV/AIDS, with a substantial degree of non-compliance to randomized treatment (Nelfinavir versus placebo) and with left censoring of the outcome variable (HIV RNA concentration). We consider in detail the assumptions and implications behind the inclusion and exclusion of interactions between randomized arm and baseline covariates in modelling actual treatment received, and between treatment and baseline covariates in modelling outcome. Estimated treatment effects were sensitive to inclusion of interactions, and we show how such sensitivity can be explored and explained.     

Allowing for uncertainty due to missing data in meta-analysis--part 1: two-stage methods

Analysis of a randomized trial with missing outcome data involves untestable assumptions, such as the missing at random (MAR) assumption. Estimated treatment effects are potentially biased if these assumptions are wrong. We quantify the degree of departure from the MAR assumption by the informative missingness odds ratio (IMOR). We incorporate prior beliefs about the IMOR in a Bayesian pattern-mixture model and derive a point estimate and standard error that take account of the uncertainty about the IMOR. In meta-analysis, this model should be used for four separate sensitivity analyses which explore the impact of IMORs that either agree or contrast across trial arms on pooled results via their effects on point estimates or on standard errors. We also propose a variance inflation factor that can be used to assess the influence of trials with many missing outcomes on the meta-analysis. We illustrate the methods using a meta-analysis on psychiatric interventions in deliberate self-harm.     

Randomized clinical trials with added rescue medication: some approaches to their analysis and interpretation

Patients in some randomized clinical trials may start additional non-randomized medication because of an exacerbation of symptoms or insufficient therapeutic effect. Typically this rescue medication reduces the observed treatment effect in intention-to-treat analysis. We discuss methods of analysis which take account of rescue medication in order to achieve a more meaningful comparison of the randomized treatments, focusing on trials with a repeated quantitative outcome. Ignoring all data after rescue is likely to be biased because rescued patients are a highly selected group. Instead we propose using methods based on ranks or multilevel models. The rank-based methods assume that rescued patients have especially bad underlying outcomes. The multilevel regression model relates a patient's outcome to allocated treatment and rescue status at each time, and requires correct modelling of all prognostic factors which predict starting rescue medication and of the covariance between outcomes measured at different times. We also describe sensitivity analyses over a range of possible models for the effect of rescue medication. We illustrate these methods in a trial in Parkinson's disease. It appears that adjustment for rescue medication will not radically alter the randomized treatment comparison unless rescue medication is substantially imbalanced between randomized groups and has a substantial effect on the outcome.     

STATISTICAL REPORTING OF CLINICAL TRIALS WITH INDIVIDUAL CHANGES FROM ALLOCATED TREATMENT

We consider clinical trials in which information is available about subjects' treatment changes after randomization. To understand whether any difference between randomized groups in the intention-to-treat analysis can be explained by such treatment changes, we need analysis strategies which take account of treatment actually received. Selection bias is then a potentially serious problem. We relate risk in a time-dependent proportional hazards model to current treatment, with treatment combinations coded in two alternative ways. To reduce selection bias, treatment history (number of treatments dropped) and baseline covariates can be added to the model. Including current risk markers would also reduce selection bias but makes interpretation difficult. The methods are illustrated using data from the British Medical Research Council (MRC) elderly hypertension trial, with time to cardiovascular death as an outcome. Results for the comparison of diuretic and beta-blocker treatment are similar in all analyses, suggesting that selection bias is small and adding support to the hypothesis that the observed treatment differences are due to the randomized treatments themselves.     

Formulating causal questions and principled statistical answers

Although review papers on causal inference methods are now available, there is a lack of introductory overviews on what they can render and on the guiding criteria for choosing one particular method. This tutorial gives an overview in situations where an exposure of interest is set at a chosen baseline (“point exposure”) and the target outcome arises at a later time point. We first phrase relevant causal questions and make a case for being specific about the possible exposure levels involved and the populations for which the question is relevant. Using the potential outcomes framework, we describe principled definitions of causal effects and of estimation approaches classified according to whether they invoke the no unmeasured confounding assumption (including outcome regression and propensity score-based methods) or an instrumental variable with added assumptions. We mainly focus on continuous outcomes and causal average treatment effects. We discuss interpretation, challenges, and potential pitfalls and illustrate application using a “simulation learner,” that mimics the effect of various breastfeeding interventions on a child's later development. This involves a typical simulation component with generated exposure, covariate, and outcome data inspired by a randomized intervention study. The simulation learner further generates various (linked) exposure types with a set of possible values per observation unit, from which observed as well as potential outcome data are generated. It thus provides true values of several causal effects. R code for data generation and analysis is available on www.ofcaus.org , where SAS and Stata code for analysis is also provided.     

Confidence interval estimation for the changepoint of treatment stratification in the presence of a qualitative covariate-treatment interaction

The goal in stratified medicine is to administer the “best” treatment to a patient. Not all patients might benefit from the same treatment; the choice of best treatment can depend on certain patient characteristics. In this article, it is assumed that a time-to-event outcome is considered as a patient-relevant outcome and a qualitative interaction between a continuous covariate and treatment exists, ie, that patients with different values of one specific covariate should be treated differently. We suggest and investigate different methods for confidence interval estimation for the covariate value, where the treatment recommendation should be changed based on data collected in a randomized clinical trial. An adaptation of Fieller's theorem, the delta method, and different bootstrap approaches (normal, percentile-based, wild bootstrap) are investigated and compared in a simulation study. Extensions to multivariable problems are presented and evaluated. We observed appropriate confidence interval coverage following Fieller's theorem irrespective of sample size but at the cost of very wide or even infinite confidence intervals. The delta method and the wild bootstrap approach provided the smallest intervals but inadequate coverage for small to moderate event numbers, also depending on the location of the true changepoint. For the percentile-based bootstrap, wide intervals were observed, and it was slightly conservative regarding coverage, whereas the normal bootstrap did not provide acceptable results for many scenarios. The described methods were also applied to data from a randomized clinical trial comparing two treatments for patients with symptomatic, severe carotid artery stenosis, considering patient's age as predictive marker.     

Adjusting treatment comparisons to account for non-randomized interventions: an example from an angina trial

In a clinical trial where some subjects receive one or more non-randomized interventions during follow-up, primary interest is in the effect of the overall treatment strategies as implemented, but it may also be of interest to adjust treatment comparisons for non-randomized interventions. We consider non-randomized interventions, especially surgical procedures, which only occur when the outcome would otherwise have been poor. Focusing on an outcome measured repeatedly over time, we describe the variety of questions that may be addressed by an adjusted analysis. The adjusted analyses involve new outcome variables defined in terms of the observed outcomes and the history of non-randomized intervention. We also show how to check the assumption that the outcome would otherwise have been poor, and how to do a sensitivity analysis. We apply these methods to a clinical trial comparing initial angioplasty with medical management in patients with angina. We find that the initial benefit of a single angioplasty in reducing angina tends to disappear with time, but a policy of additional interventions as required yields a benefit that is maintained over 4 years. Such methods may be of interest to many pragmatic randomized trials in which the effects of the initial randomized treatments and the effects of the overall treatment strategies as implemented are both of interest.     

Randomization and baseline transmission in vaccine field trials

In randomized trials, the treatment assignment mechanism is independent of the outcome of interest and other covariates thought to be relevant in determining this outcome. It also allows, on average, for a balanced distribution of these covariates in the vaccine and placebo groups. Randomization, however, does not guarantee that the estimated effect is an unbiased estimate of the biological effect of interest. We show how exposure to infection can be a confounder even in randomized vaccine field trials. Based on a simple model of the biological efficacy of interest, we extend the arguments on comparability and collapsibility to examine the limits of randomization to control for unmeasured covariates. Estimates from randomized, placebo-controlled Phase III vaccine field trials that differ in baseline transmission are not comparable unless explicit control for baseline transmission is taken into account.     

Extensions to the two‐stage randomized trial design for testing treatment,self‐selection,and treatment preference effects to binary outcomes

While traditional clinical trials seek to determine treatment efficacy within a specified population, they often ignore the role of a patient's treatment preference on his or her treatment response. The two‐stage (doubly) randomized preference trial design provides one approach for researchers seeking to disentangle preference effects from treatment effects. Currently, this two‐stage design is limited to the design and analysis of continuous outcome variables; in this presentation, we extend this current design to include binary variables. We present test statistics for testing preference, selection, and treatment effects in a two‐stage randomized design with a binary outcome measure, with and without stratification. We also derive closed‐form sample size formulas to indicate the number of patients needed to detect each effect. A series of simulation studies explore the properties and efficiency of both the unstratified and stratified two‐stage randomized trial designs. Finally, we demonstrate the applicability of these methods using an example of a trial of Hepatitis C treatment.     

检出偏倚:不同研究设计的结构分析

检出偏倚是一种常见的信息偏倚,在Horwitz绝经后服用雌激素与子宫内膜癌之间的关联研究中首次被提出,并广泛地存在于各类流行病学研究中。本文应用有向无环图,分析暴露-结局间的效应,并以测量的暴露-测量的结局间的关联来估计;检出偏倚的产生,实质上是从测量的暴露至测量的结局之间存在着的额外的、与研究兴趣无关的开放路径所致。通过对不同研究设计如队列研究、随机对照临床试验和病例对照研究等进行具体分析,了解检出偏倚的产生机制及其对效应估计(或关联)的可能影响。     

Doubly robust inference for targeted minimum loss–based estimation in randomized trials with missing outcome data

Missing outcome data is a crucial threat to the validity of treatment effect estimates from randomized trials. The outcome distributions of participants with missing and observed data are often different, which increases bias. Causal inference methods may aid in reducing the bias and improving efficiency by incorporating baseline variables into the analysis. In particular, doubly robust estimators incorporate 2 nuisance parameters: the outcome regression and the missingness mechanism (ie, the probability of missingness conditional on treatment assignment and baseline variables), to adjust for differences in the observed and unobserved groups that can be explained by observed covariates. To consistently estimate the treatment effect, one of these nuisance parameters must be consistently estimated. Traditionally, nuisance parameters are estimated using parametric models, which often precludes consistency, particularly in moderate to high dimensions. Recent research on missing data has focused on data‐adaptive estimation to help achieve consistency, but the large sample properties of such methods are poorly understood. In this article, we discuss a doubly robust estimator that is consistent and asymptotically normal under data‐adaptive estimation of the nuisance parameters. We provide a formula for an asymptotically exact confidence interval under minimal assumptions. We show that our proposed estimator has smaller finite‐sample bias compared to standard doubly robust estimators. We present a simulation study demonstrating the enhanced performance of our estimators in terms of bias, efficiency, and coverage of the confidence intervals. We present the results of an illustrative example: a randomized, double‐blind phase 2/3 trial of antiretroviral therapy in HIV‐infected persons.     

A Bayesian approach for correcting exposure misclassification in meta-analysis

In observational studies, misclassification of exposure is ubiquitous and can substantially bias the estimated association between an outcome and an exposure. Although misclassification in a single observational study has been well studied, few papers have considered it in a meta-analysis. Meta-analyses of observational studies provide important evidence for health policy decisions, especially when large randomized controlled trials are unethical or unavailable. It is imperative to account properly for misclassification in a meta-analysis to obtain valid point and interval estimates. In this paper, we propose a novel Bayesian approach to filling this methodological gap. We simultaneously synthesize two (or more) meta-analyses, with one on the association between a misclassified exposure and an outcome (main studies), and the other on the association between the misclassified exposure and the true exposure (validation studies). We extend the current scope for using external validation data by relaxing the “transportability” assumption by means of random effects models. Our model accounts for heterogeneity between studies and can be extended to allow different studies to have different exposure measurements. The proposed model is evaluated through simulations and illustrated using real data from a meta-analysis of the effect of cigarette smoking on diabetic peripheral neuropathy.     

Diagnostics for confounding in PK/PD models for oxcarbazepine

One type of pharmacokinetic/pharmacodynamic (PK/PD) relationship that is used to characterize the therapeutic action of a drug is the relationship between some univariate summary of the plasma-concentration-versus-time profile and the drug effect on a response outcome. Operationally, such a relationship may be observed in a large clinical trial where randomly sampled patients are randomized to different values of the concentration summary. If, under such conditions, the relationship between concentration and effect does not depend on the dose needed to attain the target concentration, such a relationship will be called a true PK/PD relationship. When the true PK/PD relationship is assessed as an object of estimation in a dose-controlled clinical trial (i.e. when dose is randomized), observed drug concentration is an outcome variable. The estimated PK/PD relationship between observed outcome and observed concentration, which we then refer to as the conventional PK/PD relationship, may be biased for the true PK/PD relationship. Because of this bias, the conventional relationship is called confounded for the true one. We show that diagnostics for confounding can be devised under reasonable assumptions. We then apply these diagnostics to PK/PD assessments of adults and children on oxcarbazepine adjunctive therapy. It was necessary to demonstrate the similarity of the true PK/PD relationships of adults and children on adjunctive therapy in order to support the approval of oxcarbazepine monotherapy in children by a bridging argument.     

Sulfa use, dihydropteroate synthase mutations, and Pneumocystis jirovecii pneumonia

A systematic review was conducted to examine the associations in Pneumocystis jirovecii pneumonia (PCP) patients between dihydropteroate synthase (DHPS) mutations and sulfa or sulfone (sulfa) prophylaxis and between DHPS mutations and sulfa treatment outcome. Selection criteria included study populations composed entirely of PCP patients and mutation or treatment outcome results for all patients, regardless of exposure status. Based on 13 studies, the risk of developing DHPS mutations is higher for PCP patients receiving sulfa prophylaxis than for PCP patients not receiving sulfa prophylaxis (p < 0.001). Results are too heterogeneous (p < 0.001) to warrant a single summary effect estimate. Estimated effects are weaker after 1996 and stronger in studies that included multiple isolates per patient. Five studies examined treatment outcome. The effect of DHPS mutations on treatment outcome has not been well studied, and the few studies that have been conducted are inconsistent even as to the presence or absence of an association.     

The mediation proportion: a structural equation approach for estimating the proportion of exposure effect on outcome explained by an intermediate variable

It is often of interest to assess how much of the effect of an exposure on a response is mediated through an intermediate variable. However, systematic approaches are lacking, other than assessment of a surrogate marker for the endpoint of a clinical trial. We review a measure of "proportion explained" in the context of observational epidemiologic studies. The measure has been much debated; we show how several of the drawbacks are alleviated when exposures, mediators, and responses are continuous and are embedded in a structural equation framework. These conditions also allow for consideration of several intermediate variables. Binary or categorical variables can be included directly through threshold models. We call this measure the mediation proportion, that is, the part of an exposure effect on outcome explained by a third, intermediate variable. Two examples illustrate the approach. The first example is a randomized clinical trial of the effects of interferon-alpha on visual acuity in patients with age-related macular degeneration. In this example, the exposure, mediator and response are all binary. The second example is a common problem in social epidemiology-to find the proportion of a social class effect on a health outcome that is mediated by psychologic variables. Both the mediator and the response are composed of several ordered categorical variables, with confounders present. Finally, we extend the example to more than one mediator.     

Changes in cue reactivity following treatment for bulimia nervosa

OBJECTIVE: To examine changes in cue reactivity following cognitive-behavior therapy (CBT) for bulimia nervosa and to evaluate whether changes are associated with treatment modality or treatment outcome. METHOD: Subjects were 135 women (17-45 years old) with a current, primary diagnosis of bulimia nervosa. They were participants in a randomized clinical trial examining the additive efficacy of exposure and nonexposure-based behavior therapy to a core of CBT. Physiological, self-report, and behavioral measures of cue reactivity to individualized high-risk binge foods were obtained at pretreatment and posttreatment. Primary, secondary, and tertiary outcome measures are reported for posttreatment. RESULTS: Bulimic patients experienced significant changes in cue reactivity following treatment. With the exception of salivary reactivity, patients experienced less reactivity at posttreatment. Changes in cue reactivity were not related to treatment modality, but were related to positive treatment outcome for self-report measures of cue reactivity. DISCUSSION: Favorable treatment outcome among bulimic women is associated with low cue reactivity on self-report measures at posttreatment.     

Cue reactivity as a predictor of outcome with bulimia nervosa

The present study sought to evaluate specific hypotheses concerning the relation between cue reactivity and outcome among women with bulimia nervosa. Participants were 135 women aged between 17 and 45 years with a current, primary diagnosis of bulimia nervosa who participated in a randomized clinical trial evaluating the additive efficacy of exposure and nonexposure-based behavior therapy, to a core of cognitive behavior therapy (CBT). Physiological, self-report, and behavioral measures of cue reactivity to individualized high-risk binge foods were obtained at pretreatment and posttreatment. Primary, secondary, and tertiary outcome measures are reported for posttreatment and six-month follow-up. Self-report measures of cue reactivity at posttreatment were significantly positively associated with symptomatology at posttreatment. Cue reactivity at posttreatment was significantly positively associated with symptomatology at 6-month follow-up. However, cue reactivity at posttreatment did not contribute to the prediction of outcome at follow-up over and above posttreatment outcome. The notion that pretreatment cue reactivity may predict which treatment modality will be most beneficial (exposure or nonexposure-based treatment), as measured by reductions in symptomatology at posttreatment could not be supported. Implications for future research are discussed.     

Estimating treatment effects in randomized clinical trials in the presence of non-compliance

In clinical trials where patients are randomized between two treatment arms, not all patients comply with the treatment they were randomly assigned to. The reasons for (non)compliance may be associated with the outcome variable and thereby act as confounders. The standard way of analysing such trials is by the 'intention-to-treat' principle, which allows the use of permutation tests. Conclusions drawn from such tests do not depend on untested assumptions such as absence of confounding. However, this approach may yield biased estimators for the causal effects of treatments. We consider the estimation of such effects for clinical trials where non-compliers can be considered to have switched to the other trial arm. The most important example of this is the placebo-controlled clinical trial where no substantial placebo effects are anticipated. We consider the situation where the relationship between compliance, and thus treatment received, and outcome is influenced by unobserved confounders. The residual of the regression of the actual treatment indicator variable on the randomization arm indicator variable is shown to 'intercept' the effect of such confounders. Inclusion of this residual in a multivariate analysis, in conjunction with the treatment indicator variable, should thus adjust for confounding. Examples are given. In those examples, the results are similar to those obtained by more complex methods.     

Causality in medicine: getting back to the Hill top

Evidence from randomized controlled trials (RCTs) is almost universally regarded as setting the "gold standard" for medical evidence. Claims that RCTs carry special epistemic weight are often based on the notion that evidence from randomized studies, and only such evidence, can establish that any observed connection between treatment and outcome was caused by the treatment on trial. Any non-randomized trial, on the contrary, inevitably leaves open the possibility that there is some underlying connection independent of receiving the treatment between outcome and one or more differentiating characteristics between those in the experimental and control groups; and hence inevitably leaves open the possibility that treatment and an observed better outcome were "merely correlated" rather than directly causally connected. Here I scrutinize this argument and point towards a more tenable and more modest position by recalling some of the forgotten insights of the RCT pioneer, Austin Bradford Hill.     

Up-front versus sequential randomizations for inference on adaptive treatment strategies

Adaptive treatment strategies are useful in the treatment of chronic diseases such as AIDS and cancer because they allow tailoring the treatment to a patient's need and disease status. We consider two randomization schemes for clinical trials that are commonly used to design studies comparing adaptive treatment strategies, namely, up-front randomization and sequential randomization. Up-front randomization is the classical method of randomization where patients are randomized at the beginning of the study to pre-specified treatment strategies. In sequentially randomized trials, patients are randomized sequentially to available treatment options over the duration of the therapy as they become eligible to receive subsequent treatments. We compare the efficiency and the power of the traditional up-front randomized trials with that of sequentially randomized trials designed for comparing adaptive treatment strategies based on a continuous outcome. The analytical and simulation results indicate that, when properly analyzed, sequentially randomized trials are more efficient and powerful than up-front randomized trials.